Thirty-three senators — including some high-profile Republicans — have now signed on to bipartisan legislation to create a separate military legal command to prosecute serious crimes.

GOP Sens. Rand Paul of Kentucky, Ted Cruz of Texas and Charles Grassley of Iowa have joined Democrats Kirsten Gillibrand of New York and Barbara Boxer of California in support for a measure that attempts to remove the military chain of command from decisions about prosecution and sentencing for crimes not directly related to military duties.

Sex crimes such as rape and sexual assault are the chief reasons the Military Justice Improvement Act was proposed, but it would apply to most offenses where a service member faced a year or longer in jail as the possible punishment, unless it involves military-specific offenses such as failure to obey an order or being absent without leave.

Gillibrand, chairwoman of the Senate Armed Services Committee’s personnel panel, said rape and sexual assault appear to be under-reported in the military because of fear of retaliation for coming forward and a belief that a command will not fully investigate.

Making decisions about the investigation, prosecution and punishment outside of the chain of command could lead more victims to come forward, she said.

At a Tuesday press conference to announce his support, Paul said he believes “victims of assault may be deterred if they have to report it to their boss.”

Cruz said the failure to report crimes makes them difficult to stop. “We can have no prosecution, no deterrence without reporting of crime,” he said.

The Senate is expected to take up the legislation later this year during debate on the 2014 defense authorization bill. While support is growing, it is short of the 51 votes needed to pass as an amendment to the bill, and it faces some big obstacles, including opposition from Sen. Carl Levin, D-Mich., the armed services committee chairman, and from the Joint Chiefs of Staff.

However, Sen. Richard Blumenthal, D-Conn., one of the original cosponsors, said he felt momentum was building, with the possibility of not getting just a majority of the Senate on board but also a filibuster-proof 60 votes.

Senate passage of the proposal would not guarantee it would become law. A final version of the bill would have to be worked out in negotiations with the House Armed Services Committee, where there is little support for an independent military justice command.